Properties

Label 3630.23
Modulus $3630$
Conductor $1815$
Order $44$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(3630)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([22,33,28]))
 
pari: [g,chi] = znchar(Mod(23,3630))
 

Basic properties

Modulus: \(3630\)
Conductor: \(1815\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1815}(23,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3630.bi

\(\chi_{3630}(23,\cdot)\) \(\chi_{3630}(287,\cdot)\) \(\chi_{3630}(353,\cdot)\) \(\chi_{3630}(617,\cdot)\) \(\chi_{3630}(683,\cdot)\) \(\chi_{3630}(947,\cdot)\) \(\chi_{3630}(1013,\cdot)\) \(\chi_{3630}(1277,\cdot)\) \(\chi_{3630}(1343,\cdot)\) \(\chi_{3630}(1607,\cdot)\) \(\chi_{3630}(1673,\cdot)\) \(\chi_{3630}(2003,\cdot)\) \(\chi_{3630}(2267,\cdot)\) \(\chi_{3630}(2333,\cdot)\) \(\chi_{3630}(2597,\cdot)\) \(\chi_{3630}(2927,\cdot)\) \(\chi_{3630}(2993,\cdot)\) \(\chi_{3630}(3257,\cdot)\) \(\chi_{3630}(3323,\cdot)\) \(\chi_{3630}(3587,\cdot)\)

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Values on generators

\((1211,727,3511)\) → \((-1,-i,e\left(\frac{7}{11}\right))\)

Values

\(-1\)\(1\)\(7\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{9}{44}\right)\)\(e\left(\frac{23}{44}\right)\)\(e\left(\frac{19}{44}\right)\)\(e\left(\frac{7}{22}\right)\)\(e\left(\frac{13}{44}\right)\)\(e\left(\frac{9}{11}\right)\)\(e\left(\frac{8}{11}\right)\)\(e\left(\frac{21}{44}\right)\)\(e\left(\frac{3}{22}\right)\)\(e\left(\frac{7}{44}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{44})\)
Fixed field: Number field defined by a degree 44 polynomial